A New Numerical Technique for Quasi-Linear Hyperbolic Systems of Conservation Laws

A New Numerical Technique for Quasi-Linear Hyperbolic Systems of Conservation Laws

Toro, E.F.

Cranfield Institute of Technology, College of Aeronautics

1986-12-31

A new computational method for hyperbolic conservation laws in one space dimension is presented. This technique is based on the Random Choice Method (RCM). The first step is exactly as in RCM with secondary grid, whereby intercell values at half time levels are provided. The second step completes the solution at time level n 1 via a finite difference procedure in which intercell fluxes are evaluated using the RCM solution of the first step. The method can be interpreted as a random generalisation of Godunov's method or as a random version of the Richtmeyer two-step Lax-Wendroff method. For the linear advection equation the method can be shown to be second order accurate. Application to the Euler equations, a detonation analogue (consisting of the Burger's equation plus chemical reaction) and the linear advection equation show that results are \/ery similar to those obtained by the Lax-Wendroff method. Thus for smooth flows or even for flows containing mild discontinuities the higher order method (HORCM) performs very satisfactorily. More significantly, the new method has the potential for further development that can result in a technique capable of providing higher order representation of smooth parts of the flow and absolutely sharp discontinuities such as shocks and contacts. Preliminary results from applications to various test problems are very encouraging. Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

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Cranfield Institute of Technology

College of Aeronautics Report 8626

Aerospace Engineering Reports

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(c) 1986 Cranfield Institute of Technology